Tottenham Hotspur loiter on the fringe of the Champions League places again, though even in victory this was a contest to leave Tim Sherwood scratching his head. The Spurs head coach is enjoying a crash course in Premier League management and this game took him to extremes: from fury at his side's initial shortcomings to relief in victory, presumably via a few second thoughts over the logic of selling Jermain Defoe.

The England striker was afforded 32 minutes and duly scored his first Premier League goal of the season to make safe a win that had initially felt unlikely. Defoe might have been flagged for offside but, hovering with intent, he pounced as Jonathan Parr and Damien Delaney failed to clear Aaron Lennon's pass. The finish was tucked crisply over Julián Speroni and celebrated with gusto – and, given how ineffective Roberto Soldado had been before his withdrawal, the 31-year-old's £6m sale to Toronto appears even riskier.

"I know Jermain will score wherever he plays, whatever league he plays in," Sherwood said. "If he doesn't score he gets the hump, but he'll go home happy tonight. He warmed up on the touchline like an Olympic athlete out there, up and down like a Trojan. I saw the appetite he was showing to come on. He made my mind up for me about bringing him on." The Premier League's loss will be Major League Soccer's gain.

There are likely to be a few more reminders before Defoe departs for Canada at the end of February, with his impact required here, even if Crystal Palace had blown their big chance by then. There had been times in the first half –when Spurs had been harried off their game and the visitors cut them apart from flank to centre – when Tony Pulis must have contemplated his side breaking free of the bottom three. They actually ended the afternoon beaten, bottom and rueful of missed opportunities.

Their clearest was a penalty born of Delaney's leggy burst from deep and slipped pass to Marouane Chamakh, with Mousa Dembélé's clumsy challenge yielding the foul. The striker indicated he wished to take the kick, though Jason Puncheon had scored from the spot in his team's last league outing, on New Year's Day, and took responsibility again. He ambled up to the ball, indecision gripping, and sliced it horrendously high and wide. The winger is still waiting for his loan deal from Southampton to be made permanent; this miss was untimely.

Had their delivery thereafter been more accurate, Palace might still have flourished while Sherwood flapped in livid disbelief on the sidelines. But too many crosses were over-hit and, when Palace did gain sight of goal, their finishing was awry. Chamakh, who would be denied late on by Hugo Lloris, might have scored from close range, only for his shot to strike Yannick Bolasie. Adlène Guedioura, meanwhile, battered the ball just wide from distance. This has been the story of Palace's season, and bite must be recruited this month if they are to survive.Spurs had been there for the taking, the tidy Nabil Bentaleb alone in impressing and striking the woodwork from distance. They were unlikely to prove as accommodating after the break, once Sherwood had made his displeasure known. "The manager was really angry at half-time," said Christian Eriksen, whose up-turn in industry epitomised that of his team. When substitute Kyle Naughton flung a pass forward and Emmanuel Adebayor outjumped Danny Gabbidon and Adrian Mariappa, there was Eriksen, unchecked, to thump the ball into the top corner with Speroni exposed.

"We'd been taken a bit by surprise by Palace," said Sherwood, who lost Kyle Walker to a calf strain. "But in the second half we matched them for desire and effort, and our quality shone through."

The lead gave Spurs the opportunity to dictate the tempo, Palace's energy levels having dipped, with Eriksen revelling. Defoe's cameo added to their firepower, the England forward instantly menacing. He had already belted one shot beyond the far post when he escaped the linesman's flag to give the scoreline an air of comfort.